A Course in Modern Geometries

A Course in Modern Geometries is a textbook designed for mathematics students at the junior and senior levels, including those aspiring to teach at secondary schools. The book provides a comprehensive introduction to various geometric concepts, starting with finite geometries in an axiomatic framework. It covers both synthetic and analytical approaches to geometry, including classical Euclidean geometry as well as non-Euclidean geometries. The chapters are structured to address both theoretical and practical aspects of geometry, with a particular focus on symmetry, isometries, and the application of matrices. Additionally, a new chapter discusses chaos theory and fractal geometry, encouraging readers to explore the connections between different mathematical disciplines. Each chapter includes recommended resources for applications in art and history, making the book a valuable teaching tool.